#!/usr/bin/env python3




##################################################
## DEPENDENCIES
import sys
import os
import os.path
try:
    import builtins as builtin
except ImportError:
    import __builtin__ as builtin
from os.path import getmtime, exists
import time
import types
from Cheetah.Version import MinCompatibleVersion as RequiredCheetahVersion
from Cheetah.Version import MinCompatibleVersionTuple as RequiredCheetahVersionTuple
from Cheetah.Template import Template
from Cheetah.DummyTransaction import *
from Cheetah.NameMapper import NotFound, valueForName, valueFromSearchList, valueFromFrameOrSearchList
from Cheetah.CacheRegion import CacheRegion
import Cheetah.Filters as Filters
import Cheetah.ErrorCatchers as ErrorCatchers
from Cheetah.compat import unicode
from xpdeint.Segments.Integrators._Stepper import _Stepper

##################################################
## MODULE CONSTANTS
VFFSL=valueFromFrameOrSearchList
VFSL=valueFromSearchList
VFN=valueForName
currentTime=time.time
__CHEETAH_version__ = '3.2.3'
__CHEETAH_versionTuple__ = (3, 2, 3, 'final', 0)
__CHEETAH_genTime__ = 1558054970.399553
__CHEETAH_genTimestamp__ = 'Fri May 17 11:02:50 2019'
__CHEETAH_src__ = '/home/mattias/xmds-2.2.3/admin/staging/xmds-3.0.0/xpdeint/Segments/Integrators/RK9Stepper.tmpl'
__CHEETAH_srcLastModified__ = 'Thu Apr  4 16:29:24 2019'
__CHEETAH_docstring__ = 'Autogenerated by Cheetah: The Python-Powered Template Engine'

if __CHEETAH_versionTuple__ < RequiredCheetahVersionTuple:
    raise AssertionError(
      'This template was compiled with Cheetah version'
      ' %s. Templates compiled before version %s must be recompiled.'%(
         __CHEETAH_version__, RequiredCheetahVersion))

##################################################
## CLASSES

class RK9Stepper(_Stepper):

    ##################################################
    ## CHEETAH GENERATED METHODS


    def __init__(self, *args, **KWs):

        super(RK9Stepper, self).__init__(*args, **KWs)
        if not self._CHEETAH__instanceInitialized:
            cheetahKWArgs = {}
            allowedKWs = 'searchList namespaces filter filtersLib errorCatcher'.split()
            for k,v in KWs.items():
                if k in allowedKWs: cheetahKWArgs[k] = v
            self._initCheetahInstance(**cheetahKWArgs)
        

    def name(self, **KWS):



        ## Generated from @def name: RK9 at line 26, col 1.
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        write('''RK9''')
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def localInitialise(self, **KWS):



        ## CHEETAH: generated from @def localInitialise at line 39, col 1.
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        # 
        _v = super(RK9Stepper, self).localInitialise()
        if _v is not None: write(_filter(_v))
        # 
        write('''
// Runge Kutta method constants
real _a_raw[16];
real _a[16];
real _b[16][16];
real _c[16];
real _d[16];

for(unsigned long _i0=0; _i0 < 16; _i0++)
{
  _a_raw[_i0] = _c[_i0] = _d[_i0] = 0.0;
  for(unsigned long _i1=0; _i1 < 16; _i1++)
   _b[_i0][_i1] = 0.0;
}

_a_raw[1]  = 0.02173913043478260869565217391304347;
_a_raw[2]  = 0.09629581047800066670113001679819925;
_a_raw[3]  = 0.14444371571700100005169502519729888;
_a_raw[4]  = 0.52205882352941176470588235294117647;
_a_raw[5]  = 0.22842443612863469578031459099794265;
_a_raw[6]  = 0.54360353589933733219171338103002937;
_a_raw[7]  = 0.64335664335664335664335664335664335;
_a_raw[8]  = 0.48251748251748251748251748251748251;
_a_raw[9]  = 0.06818181818181818181818181818181818;
_a_raw[10] = 0.25060827250608272506082725060827250;
_a_raw[11] = 0.66736715965600568968278165443304378;
_a_raw[12] = 0.85507246376811594202898550724637681;
_a_raw[13] = 0.89795918367346938775510204081632653;
_a_raw[14] = 1.0;
_a_raw[15] = 1.0;

_a[0]=0.0;
for(unsigned long _i0=1; _i0 < 16; _i0++)
  _a[_i0] = _a_raw[_i0] - _a_raw[_i0-1];

_b[1][0]   = 1.0/46.0;
_b[2][0]   =-0.11698050118114486205818241524969622;
_b[2][1]   = 0.21327631165914552875931243204789548;
_b[3][0]   = 0.03611092892925025001292375629932472;
_b[3][2]   = 0.10833278678775075003877126889797416;
_b[4][0]   = 1.57329743908138605107331820072051125;
_b[4][2]   =-5.98400943754042002888532938159655553;
_b[4][3]   = 4.93277082198844574251789353381722074;
_b[5][0]   = 0.05052046351120380909008334360006234;
_b[5][3]   = 0.17686653884807108146683657390397612;
_b[5][4]   = 0.00103743376935980522339467349390418;
_b[6][0]   = 0.10543148021953768958529340893598138;
_b[6][3]   =-0.16042415162569842979496486916719383;
_b[6][4]   = 0.11643956912829316045688724281285250;
_b[6][5]   = 0.48215663817720491194449759844838932;
_b[7][0]   = 0.07148407148407148407148407148407148;
_b[7][5]   = 0.32971116090443908023196389566296464;
_b[7][6]   = 0.24216141096813279233990867620960722;
_b[8][0]   = 0.07162368881118881118881118881118881;
_b[8][5]   = 0.32859867301674234161492268975519694;
_b[8][6]   = 0.11622213117906185418927311444060725;
_b[8][7]   =-0.03392701048951048951048951048951048;
_b[9][0]   = 0.04861540768024729180628870095388582;
_b[9][5]   = 0.03998502200331629058445317782406268;
_b[9][6]   = 0.10715724786209388876739304914053506;
_b[9][7]   =-0.02177735985419485163815426357369818;
_b[9][8]   =-0.10579849950964443770179884616296721;
_b[10][0]  =-0.02540141041535143673515871979014924;
_b[10][5]  = 1.0/30.0;
_b[10][6]  =-0.16404854760069182073503553020238782;
_b[10][7]  = 0.03410548898794737788891414566528526;
_b[10][8]  = 0.15836825014108792658008718465091487;
_b[10][9]  = 0.21425115805975734472868683695127609;
_b[11][0]  = 0.00584833331460742801095934302256470;
_b[11][5]  =-0.53954170547283522916525526480339109;
_b[11][6]  = 0.20128430845560909506500331018201158;
_b[11][7]  = 0.04347222773254789483240207937678906;
_b[11][8]  =-0.00402998571475307250775349983910179;
_b[11][9]  = 0.16541535721570612771420482097898952;
_b[11][10] = 0.79491862412512344573322086551518180;
_b[12][0]  =-0.39964965968794892497157706711861448;
_b[12][5]  =-3.79096577568393158554742638116249372;
_b[12][6]  =-0.40349325653530103387515807815498044;
_b[12][7]  =-2.82463879530435263378049668286220715;
_b[12][8]  = 1.04226892772185985533374283289821416;
_b[12][9]  = 1.12510956420436603974237036536924078;
_b[12][10] = 3.32746188718986816186934832571938138;
_b[12][11] = 2.77897957186355606325818219255783627;
_b[13][0]  = 0.39545306350085237157098218205756922;
_b[13][5]  = 5.82534730759650564865380791881446903;
_b[13][6]  =-0.36527452339161313311889856846974452;
_b[13][7]  = 1.18860324058346533283780076203192232;
_b[13][8]  = 0.57970467638357921347110271762687972;
_b[13][9]  =-0.86824862589087693262676988867897834;
_b[13][10] =-5.20227677296454721392873650976792184;
_b[13][11] =-0.79895541420753382543211121058675915;
_b[13][12] = 0.14360623206363792632792463778889008;
_b[14][0]  = 8.49173149061346398013352206978380938;
_b[14][5]  = 86.32213734729036800877634194386790750;
_b[14][6]  = 1.02560575501091662034511526187393241;
_b[14][7]  = 85.77427969817339941806831550695235092;
_b[14][8]  =-13.98699305104110611795532466113248067;
_b[14][9]  =-20.71537405501426352265946477613161883;
_b[14][10] =-72.16597156619946800281180102605140463;
_b[14][11] =-76.71211139107806345587696023064419687;
_b[14][12] = 4.22319427707298828839851258893735507;
_b[14][13] =-1.25649850482823521641825667745565428;
_b[15][0]  =-0.42892119881959353241190195318730008;
_b[15][5]  =-9.16865700950084689999297912545025359;
_b[15][6]  = 1.08317616770620939241547721530003920;
_b[15][7]  =-1.23501525358323653198215832293981810;
_b[15][8]  =-1.21438272617593906232943856422371019;
_b[15][9]  = 1.37226168507232166621351243731869914;
_b[15][10] = 9.15723239697162418155377135344394113;
_b[15][11] = 1.30616301842220047563298585480401671;
_b[15][12] =-0.25285618808937955976690569433069974;
_b[15][13] = 0.38099910799663987066763679926508552;

_c[0]  = 0.01490902081978461022483617102382552;
_c[7]  =-0.20408044692054151258349120934134791;
_c[8]  = 0.22901438600570447264772469337066476;
_c[9]  = 0.12800558251147375669208211573729202;
_c[10] = 0.22380626846054143649770066956485937;
_c[11] = 0.39553165293700054420552389156421651;
_c[12] = 0.05416646758806981196568364538360743;
_c[13] = 0.12691439652445903685643385312168037;
_c[14] =-0.00052539244262118876455834655383035;
_c[15] = 1.0/31.0;

_d[0] = 1.0-_b[15][5]/_b[14][5];
_d[1] = _b[15][0]-_b[14][0]*_b[15][5]/_b[14][5];
_d[2] = _b[15][5]/_b[14][5];
_d[3] = _b[15][6]-_b[14][6]*_b[15][5]/_b[14][5];
_d[4] = _b[15][7]-_b[14][7]*_b[15][5]/_b[14][5];
_d[5] = _b[15][8]-_b[14][8]*_b[15][5]/_b[14][5];
_d[6] = _b[15][9]-_b[14][9]*_b[15][5]/_b[14][5];
_d[7] = _b[15][10]-_b[14][10]*_b[15][5]/_b[14][5];
_d[8] = _b[15][11]-_b[14][11]*_b[15][5]/_b[14][5];
_d[9] = _b[15][12]-_b[14][12]*_b[15][5]/_b[14][5];
_d[10] = _b[15][13]-_b[14][13]*_b[15][5]/_b[14][5];
''')
        # 
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def singleIntegrationStep(self, function, **KWS):



        ## CHEETAH: generated from @def singleIntegrationStep($function) at line 184, col 1.
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        # 
        arguments = {'_step': '_step'}
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 187, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 187, col 1.
        write('''
// Step 1

''')
        _v = VFFSL(SL,"copyVectors",False)(VFFSL(SL,"integrationVectors",True), '_akafield') # "${copyVectors($integrationVectors, '_akafield')}" on line 191, col 1
        if _v is not None: write(_filter(_v, rawExpr="${copyVectors($integrationVectors, '_akafield')}")) # from line 191, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 193, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 194, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 194, col 9.
            write(''' = _''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 194, col 25
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 194, col 25.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function)}" on line 197, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 1, parentFunction=function)}")) # from line 197, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}" on line 200, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}")) # from line 200, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 201, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 201, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 203, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 204, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 204, col 9.
            write(''' = _akafield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 204, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 204, col 34.
            write(''';
''')
        write('''
// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 208, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 208, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +1, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}" on line 211, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction=function)}")) # from line 211, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 212, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 212, col 1.
        write('''
// Step 2

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 216, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 216, col 1.
        write(''' += _a[1]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[1][0]*_akafield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[1][0]*_akafield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 218, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 222, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 223, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 223, col 9.
            write(''' = _akbfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 223, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 223, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function)}" on line 226, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 2, parentFunction=function)}")) # from line 226, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -2, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -2, parentFunction=function)}" on line 229, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -2, parentFunction=function)}")) # from line 229, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 232, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 232, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +2, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +2, parentFunction=function)}" on line 235, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +2, parentFunction=function)}")) # from line 235, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 236, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 236, col 1.
        write('''
// Step 3

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 240, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 240, col 1.
        write(''' += _a[2]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[2][0]*_akafield_${vector.id}[$index] + _b[2][1]*_akbfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[2][0]*_akafield_${vector.id}[$index] + _b[2][1]*_akbfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 242, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 246, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 247, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 247, col 9.
            write(''' = _akcfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 247, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 247, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function)}" on line 250, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 3, parentFunction=function)}")) # from line 250, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -3, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -3, parentFunction=function)}" on line 253, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -3, parentFunction=function)}")) # from line 253, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 256, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 256, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +3, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +3, parentFunction=function)}" on line 259, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +3, parentFunction=function)}")) # from line 259, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 260, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 260, col 1.
        write('''
// Step 4

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 264, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 264, col 1.
        write(''' += _a[3]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[3][0]*_akafield_${vector.id}[$index]
    + _b[3][1]*_akbfield_${vector.id}[$index] + _b[3][2]*_akcfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[3][0]*_akafield_${vector.id}[$index]\n    + _b[3][1]*_akbfield_${vector.id}[$index] + _b[3][2]*_akcfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 266, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 271, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 272, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 272, col 9.
            write(''' = _akdfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 272, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 272, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function)}" on line 275, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 4, parentFunction=function)}")) # from line 275, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -4, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -4, parentFunction=function)}" on line 278, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -4, parentFunction=function)}")) # from line 278, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 281, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 281, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +4, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +4, parentFunction=function)}" on line 284, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +4, parentFunction=function)}")) # from line 284, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 285, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 285, col 1.
        write('''
// Step 5

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 289, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 289, col 1.
        write(''' += _a[4]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[4][0]*_akafield_${vector.id}[$index]
    + _b[4][1]*_akbfield_${vector.id}[$index] + _b[4][2]*_akcfield_${vector.id}[$index]
    + _b[4][3]*_akdfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[4][0]*_akafield_${vector.id}[$index]\n    + _b[4][1]*_akbfield_${vector.id}[$index] + _b[4][2]*_akcfield_${vector.id}[$index]\n    + _b[4][3]*_akdfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 291, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 297, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 298, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 298, col 9.
            write(''' = _akefield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 298, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 298, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function)}" on line 301, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 5, parentFunction=function)}")) # from line 301, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -5, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -5, parentFunction=function)}" on line 304, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -5, parentFunction=function)}")) # from line 304, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 307, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 307, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +5, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +5, parentFunction=function)}" on line 310, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +5, parentFunction=function)}")) # from line 310, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 311, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 311, col 1.
        write('''
// Step 6

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 315, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 315, col 1.
        write(''' += _a[5]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[5][0]*_akafield_${vector.id}[$index]
    + _b[5][3]*_akdfield_${vector.id}[$index] + _b[5][4]*_akefield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[5][0]*_akafield_${vector.id}[$index]\n    + _b[5][3]*_akdfield_${vector.id}[$index] + _b[5][4]*_akefield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 317, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 322, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 323, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 323, col 9.
            write(''' = _akifield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 323, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 323, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function)}" on line 326, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 6, parentFunction=function)}")) # from line 326, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -6, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -6, parentFunction=function)}" on line 329, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -6, parentFunction=function)}")) # from line 329, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 332, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 332, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +6, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +6, parentFunction=function)}" on line 335, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +6, parentFunction=function)}")) # from line 335, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 336, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 336, col 1.
        write('''
// Step 7

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 340, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 340, col 1.
        write(''' += _a[6]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akjfield_${vector.id}[$index] = _${vector.id}[$index] + _b[6][0]*_akafield_${vector.id}[$index]
    + _b[6][3]*_akdfield_${vector.id}[$index] + _b[6][4]*_akefield_${vector.id}[$index]
    + _b[6][5]*_akifield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akjfield_${vector.id}[$index] = _${vector.id}[$index] + _b[6][0]*_akafield_${vector.id}[$index]\n    + _b[6][3]*_akdfield_${vector.id}[$index] + _b[6][4]*_akefield_${vector.id}[$index]\n    + _b[6][5]*_akifield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 342, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 348, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 349, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 349, col 9.
            write(''' = _akjfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 349, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 349, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function)}" on line 352, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 7, parentFunction=function)}")) # from line 352, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -7, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -7, parentFunction=function)}" on line 355, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -7, parentFunction=function)}")) # from line 355, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 358, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 358, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +7, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +7, parentFunction=function)}" on line 361, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +7, parentFunction=function)}")) # from line 361, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 362, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 362, col 1.
        write('''
// Step 8

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 366, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 366, col 1.
        write(''' += _a[7]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[7][0]*_akafield_${vector.id}[$index]
    + _b[7][5]*_akifield_${vector.id}[$index] + _b[7][6]*_akjfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akbfield_${vector.id}[$index] = _${vector.id}[$index] + _b[7][0]*_akafield_${vector.id}[$index]\n    + _b[7][5]*_akifield_${vector.id}[$index] + _b[7][6]*_akjfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 368, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 373, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 374, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 374, col 9.
            write(''' = _akbfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 374, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 374, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function)}" on line 377, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 8, parentFunction=function)}")) # from line 377, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -8, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -8, parentFunction=function)}" on line 380, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -8, parentFunction=function)}")) # from line 380, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 383, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 383, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +8, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +8, parentFunction=function)}" on line 386, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +8, parentFunction=function)}")) # from line 386, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 387, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 387, col 1.
        write('''
// Step 9

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 391, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 391, col 1.
        write(''' += _a[8]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[8][0]*_akafield_${vector.id}[$index]
    + _b[8][5]*_akifield_${vector.id}[$index] + _b[8][6]*_akjfield_${vector.id}[$index]
    + _b[8][7]*_akbfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akcfield_${vector.id}[$index] = _${vector.id}[$index] + _b[8][0]*_akafield_${vector.id}[$index]\n    + _b[8][5]*_akifield_${vector.id}[$index] + _b[8][6]*_akjfield_${vector.id}[$index]\n    + _b[8][7]*_akbfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 393, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 399, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 400, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 400, col 9.
            write(''' = _akcfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 400, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 400, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function)}" on line 403, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 9, parentFunction=function)}")) # from line 403, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -9, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -9, parentFunction=function)}" on line 406, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -9, parentFunction=function)}")) # from line 406, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 409, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 409, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +9, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +9, parentFunction=function)}" on line 412, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +9, parentFunction=function)}")) # from line 412, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 413, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 413, col 1.
        write('''
// Step 10

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 417, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 417, col 1.
        write(''' += _a[9]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[9][0]*_akafield_${vector.id}[$index]
    + _b[9][5]*_akifield_${vector.id}[$index] + _b[9][6]*_akjfield_${vector.id}[$index]
    + _b[9][7]*_akbfield_${vector.id}[$index] + _b[9][8]*_akcfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akdfield_${vector.id}[$index] = _${vector.id}[$index] + _b[9][0]*_akafield_${vector.id}[$index]\n    + _b[9][5]*_akifield_${vector.id}[$index] + _b[9][6]*_akjfield_${vector.id}[$index]\n    + _b[9][7]*_akbfield_${vector.id}[$index] + _b[9][8]*_akcfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 419, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 425, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 426, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 426, col 9.
            write(''' = _akdfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 426, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 426, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function)}" on line 429, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 10, parentFunction=function)}")) # from line 429, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -10, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -10, parentFunction=function)}" on line 432, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -10, parentFunction=function)}")) # from line 432, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 435, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 435, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +10, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +10, parentFunction=function)}" on line 438, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +10, parentFunction=function)}")) # from line 438, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 439, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 439, col 1.
        write('''
// Step 11

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 443, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 443, col 1.
        write(''' += _a[10]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[10][0]*_akafield_${vector.id}[$index]
    + _b[10][5]*_akifield_${vector.id}[$index] + _b[10][6]*_akjfield_${vector.id}[$index]
    + _b[10][7]*_akbfield_${vector.id}[$index] + _b[10][8]*_akcfield_${vector.id}[$index]
    + _b[10][9]*_akdfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akefield_${vector.id}[$index] = _${vector.id}[$index] + _b[10][0]*_akafield_${vector.id}[$index]\n    + _b[10][5]*_akifield_${vector.id}[$index] + _b[10][6]*_akjfield_${vector.id}[$index]\n    + _b[10][7]*_akbfield_${vector.id}[$index] + _b[10][8]*_akcfield_${vector.id}[$index]\n    + _b[10][9]*_akdfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 445, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 452, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 453, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 453, col 9.
            write(''' = _akefield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 453, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 453, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function)}" on line 456, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 11, parentFunction=function)}")) # from line 456, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -11, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -11, parentFunction=function)}" on line 459, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -11, parentFunction=function)}")) # from line 459, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 462, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 462, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +11, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +11, parentFunction=function)}" on line 465, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +11, parentFunction=function)}")) # from line 465, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 466, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 466, col 1.
        write('''
// Step 12

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 470, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 470, col 1.
        write(''' += _a[11]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akffield_${vector.id}[$index] = _${vector.id}[$index] + _b[11][0]*_akafield_${vector.id}[$index]
    + _b[11][5]*_akifield_${vector.id}[$index] + _b[11][6]*_akjfield_${vector.id}[$index]
    + _b[11][7]*_akbfield_${vector.id}[$index] + _b[11][8]*_akcfield_${vector.id}[$index]
    + _b[11][9]*_akdfield_${vector.id}[$index] + _b[11][10]*_akefield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akffield_${vector.id}[$index] = _${vector.id}[$index] + _b[11][0]*_akafield_${vector.id}[$index]\n    + _b[11][5]*_akifield_${vector.id}[$index] + _b[11][6]*_akjfield_${vector.id}[$index]\n    + _b[11][7]*_akbfield_${vector.id}[$index] + _b[11][8]*_akcfield_${vector.id}[$index]\n    + _b[11][9]*_akdfield_${vector.id}[$index] + _b[11][10]*_akefield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 472, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 479, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 480, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 480, col 9.
            write(''' = _akffield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 480, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 480, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function)}" on line 483, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 12, parentFunction=function)}")) # from line 483, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -12, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -12, parentFunction=function)}" on line 486, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -12, parentFunction=function)}")) # from line 486, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 489, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 489, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +12, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +12, parentFunction=function)}" on line 492, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +12, parentFunction=function)}")) # from line 492, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 493, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 493, col 1.
        write('''
// Step 13

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 497, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 497, col 1.
        write(''' += _a[12]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akgfield_${vector.id}[$index] = _${vector.id}[$index] + _b[12][0]*_akafield_${vector.id}[$index]
    + _b[12][5]*_akifield_${vector.id}[$index] + _b[12][6]*_akjfield_${vector.id}[$index]
    + _b[12][7]*_akbfield_${vector.id}[$index] + _b[12][8]*_akcfield_${vector.id}[$index]
    + _b[12][9]*_akdfield_${vector.id}[$index] + _b[12][10]*_akefield_${vector.id}[$index]
    + _b[12][11]*_akffield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akgfield_${vector.id}[$index] = _${vector.id}[$index] + _b[12][0]*_akafield_${vector.id}[$index]\n    + _b[12][5]*_akifield_${vector.id}[$index] + _b[12][6]*_akjfield_${vector.id}[$index]\n    + _b[12][7]*_akbfield_${vector.id}[$index] + _b[12][8]*_akcfield_${vector.id}[$index]\n    + _b[12][9]*_akdfield_${vector.id}[$index] + _b[12][10]*_akefield_${vector.id}[$index]\n    + _b[12][11]*_akffield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 499, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 507, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 508, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 508, col 9.
            write(''' = _akgfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 508, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 508, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function)}" on line 511, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 13, parentFunction=function)}")) # from line 511, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -13, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -13, parentFunction=function)}" on line 514, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -13, parentFunction=function)}")) # from line 514, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 517, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 517, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +13, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +13, parentFunction=function)}" on line 520, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +13, parentFunction=function)}")) # from line 520, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 521, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 521, col 1.
        write('''
// Step 14

''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 525, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 525, col 1.
        write(''' += _a[13]*_step;

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akhfield_${vector.id}[$index] = _${vector.id}[$index] + _b[13][0]*_akafield_${vector.id}[$index]
    + _b[13][5]*_akifield_${vector.id}[$index] + _b[13][6]*_akjfield_${vector.id}[$index]
    + _b[13][7]*_akbfield_${vector.id}[$index] + _b[13][8]*_akcfield_${vector.id}[$index]
    + _b[13][9]*_akdfield_${vector.id}[$index] + _b[13][10]*_akefield_${vector.id}[$index]
    + _b[13][11]*_akffield_${vector.id}[$index] + _b[13][12]*_akgfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akhfield_${vector.id}[$index] = _${vector.id}[$index] + _b[13][0]*_akafield_${vector.id}[$index]\n    + _b[13][5]*_akifield_${vector.id}[$index] + _b[13][6]*_akjfield_${vector.id}[$index]\n    + _b[13][7]*_akbfield_${vector.id}[$index] + _b[13][8]*_akcfield_${vector.id}[$index]\n    + _b[13][9]*_akdfield_${vector.id}[$index] + _b[13][10]*_akefield_${vector.id}[$index]\n    + _b[13][11]*_akffield_${vector.id}[$index] + _b[13][12]*_akgfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 527, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 535, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 536, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 536, col 9.
            write(''' = _akhfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 536, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 536, col 34.
            write(''';
''')
        write('''
''')
        _v = VFFSL(SL,"callFunction",False)('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function) # "${callFunction('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function)}" on line 539, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('nonconstantIPFields', arguments, _exponent = 14, parentFunction=function)}")) # from line 539, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = -14, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = -14, parentFunction=function)}" on line 542, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = -14, parentFunction=function)}")) # from line 542, col 1.
        write('''

// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 545, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 545, col 1.
        write('''

// a_i = D(a_2*dt)[y1]
''')
        _v = VFFSL(SL,"callFunction",False)('ipEvolve', arguments, _exponent = +14, parentFunction=function) # "${callFunction('ipEvolve', arguments, _exponent = +14, parentFunction=function)}" on line 548, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('ipEvolve', arguments, _exponent = +14, parentFunction=function)}")) # from line 548, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 549, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 549, col 1.
        write('''
// Step 15 and 16 combined to reduce memory use

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[14][0]*_akafield_${vector.id}[$index]
    + _b[14][5]*_akifield_${vector.id}[$index] + _b[14][6]*_akjfield_${vector.id}[$index]
    + _b[14][7]*_akbfield_${vector.id}[$index] + _b[14][8]*_akcfield_${vector.id}[$index]
    + _b[14][9]*_akdfield_${vector.id}[$index] + _b[14][10]*_akefield_${vector.id}[$index]
    + _b[14][11]*_akffield_${vector.id}[$index] + _b[14][12]*_akgfield_${vector.id}[$index]
    + _b[14][13]*_akhfield_${vector.id}[$index];
    
  _akjfield_${vector.id}[$index] = _d[0]*_${vector.id}[$index]
      + _d[1]*_akafield_${vector.id}[$index]
      + _d[2]*_akifield_${vector.id}[$index] 
      + _d[3]*_akjfield_${vector.id}[$index] 
      + _d[4]*_akbfield_${vector.id}[$index]
      + _d[5]*_akcfield_${vector.id}[$index]
      + _d[6]*_akdfield_${vector.id}[$index]
      + _d[7]*_akefield_${vector.id}[$index]
      + _d[8]*_akffield_${vector.id}[$index]
      + _d[9]*_akgfield_${vector.id}[$index]
      + _d[10]*_akhfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""_akifield_${vector.id}[$index] = _${vector.id}[$index] + _b[14][0]*_akafield_${vector.id}[$index]\n    + _b[14][5]*_akifield_${vector.id}[$index] + _b[14][6]*_akjfield_${vector.id}[$index]\n    + _b[14][7]*_akbfield_${vector.id}[$index] + _b[14][8]*_akcfield_${vector.id}[$index]\n    + _b[14][9]*_akdfield_${vector.id}[$index] + _b[14][10]*_akefield_${vector.id}[$index]\n    + _b[14][11]*_akffield_${vector.id}[$index] + _b[14][12]*_akgfield_${vector.id}[$index]\n    + _b[14][13]*_akhfield_${vector.id}[$index];\n    \n  _akjfield_${vector.id}[$index] = _d[0]*_${vector.id}[$index]\n      + _d[1]*_akafield_${vector.id}[$index]\n      + _d[2]*_akifield_${vector.id}[$index] \n      + _d[3]*_akjfield_${vector.id}[$index] \n      + _d[4]*_akbfield_${vector.id}[$index]\n      + _d[5]*_akcfield_${vector.id}[$index]\n      + _d[6]*_akdfield_${vector.id}[$index]\n      + _d[7]*_akefield_${vector.id}[$index]\n      + _d[8]*_akffield_${vector.id}[$index]\n      + _d[9]*_akgfield_${vector.id}[$index]\n      + _d[10]*_akhfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 553, col 1.
        write('''
''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 574, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 574, col 1.
        write(''' += _a[14]*_step;

''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 576, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 577, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 577, col 9.
            write(''' = _akifield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 577, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 577, col 34.
            write(''';
''')
        write('''
// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 581, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 581, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 582, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 582, col 1.
        write('''
''')
        _v = VFFSL(SL,"propagationDimension",True) # '${propagationDimension}' on line 584, col 1
        if _v is not None: write(_filter(_v, rawExpr='${propagationDimension}')) # from line 584, col 1.
        write(''' += _a[15]*_step;

''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 586, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 587, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 587, col 9.
            write(''' = _akjfield_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 587, col 34
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 587, col 34.
            write(''';
''')
        write('''
// a_k = G[a_k, t]
''')
        _v = VFFSL(SL,"callFunction",False)('deltaA', arguments, parentFunction=function) # "${callFunction('deltaA', arguments, parentFunction=function)}" on line 591, col 1
        if _v is not None: write(_filter(_v, rawExpr="${callFunction('deltaA', arguments, parentFunction=function)}")) # from line 591, col 1.
        write('''
''')
        _v = VFFSL(SL,"transformVectorsToBasis",False)(VFFSL(SL,"integrationVectors",True), VFFSL(SL,"homeBasis",True)) # '${transformVectorsToBasis($integrationVectors, $homeBasis)}' on line 592, col 1
        if _v is not None: write(_filter(_v, rawExpr='${transformVectorsToBasis($integrationVectors, $homeBasis)}')) # from line 592, col 1.
        write('''
// Take full step

''')
        _v = VFFSL(SL,"loopOverVectorsWithInnerContentTemplate",False)(VFFSL(SL,"integrationVectors",True),
"""
_${vector.id}[$index] += _c[0]*_akafield_${vector.id}[$index] + _c[7]*_akbfield_${vector.id}[$index] + _c[8]*_akcfield_${vector.id}[$index]
    + _c[9]*_akdfield_${vector.id}[$index] + _c[10]*_akefield_${vector.id}[$index] + _c[11]*_akffield_${vector.id}[$index]
    + _c[12]*_akgfield_${vector.id}[$index] + _c[13]*_akhfield_${vector.id}[$index] + _c[14]*_akifield_${vector.id}[$index]
    + _c[15]*_akjfield_${vector.id}[$index];
""", basis = VFFSL(SL,"homeBasis",True))
        if _v is not None: write(_filter(_v, rawExpr='${loopOverVectorsWithInnerContentTemplate($integrationVectors,\n"""\n_${vector.id}[$index] += _c[0]*_akafield_${vector.id}[$index] + _c[7]*_akbfield_${vector.id}[$index] + _c[8]*_akcfield_${vector.id}[$index]\n    + _c[9]*_akdfield_${vector.id}[$index] + _c[10]*_akefield_${vector.id}[$index] + _c[11]*_akffield_${vector.id}[$index]\n    + _c[12]*_akgfield_${vector.id}[$index] + _c[13]*_akhfield_${vector.id}[$index] + _c[14]*_akifield_${vector.id}[$index]\n    + _c[15]*_akjfield_${vector.id}[$index];\n""", basis = $homeBasis)}')) # from line 596, col 1.
        write('''
''')
        for vector in VFFSL(SL,"integrationVectors",True): # generated from line 604, col 3
            write('''_active_''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 605, col 9
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 605, col 9.
            write(''' = _''')
            _v = VFFSL(SL,"vector.id",True) # '${vector.id}' on line 605, col 25
            if _v is not None: write(_filter(_v, rawExpr='${vector.id}')) # from line 605, col 25.
            write(''';
''')
        # 
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        

    def writeBody(self, **KWS):



        ## CHEETAH: main method generated for this template
        trans = KWS.get("trans")
        if (not trans and not self._CHEETAH__isBuffering and not callable(self.transaction)):
            trans = self.transaction # is None unless self.awake() was called
        if not trans:
            trans = DummyTransaction()
            _dummyTrans = True
        else: _dummyTrans = False
        write = trans.response().write
        SL = self._CHEETAH__searchList
        _filter = self._CHEETAH__currentFilter
        
        ########################################
        ## START - generated method body
        
        write('''
''')
        # 
        # RK9Stepper.tmpl
        # 
        # Created by Graham Dennis on 2007-10-20.
        # 
        # Copyright (c) 2008-2012, Graham Dennis
        # 
        # This program is free software: you can redistribute it and/or modify
        # it under the terms of the GNU General Public License as published by
        # the Free Software Foundation, either version 2 of the License, or
        # (at your option) any later version.
        # 
        # This program is distributed in the hope that it will be useful,
        # but WITHOUT ANY WARRANTY; without even the implied warranty of
        # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
        # GNU General Public License for more details.
        # 
        # You should have received a copy of the GNU General Public License
        # along with this program.  If not, see <http://www.gnu.org/licenses/>.
        # 
        write('''



''')
        # 
        #   Single integration step (RK9)
        
        ########################################
        ## END - generated method body
        
        return _dummyTrans and trans.response().getvalue() or ""
        
    ##################################################
    ## CHEETAH GENERATED ATTRIBUTES


    _CHEETAH__instanceInitialized = False

    _CHEETAH_version = __CHEETAH_version__

    _CHEETAH_versionTuple = __CHEETAH_versionTuple__

    _CHEETAH_genTime = __CHEETAH_genTime__

    _CHEETAH_genTimestamp = __CHEETAH_genTimestamp__

    _CHEETAH_src = __CHEETAH_src__

    _CHEETAH_srcLastModified = __CHEETAH_srcLastModified__

    ipPropagationStepFractions =   [ '1.000000000000000', '0.978260869565217', '0.903704189521999', '0.855556284282999',    '0.477941176470588', '0.771575563871365', '0.456396464100663', '0.356643356643357',    '0.517482517482518', '0.931818181818182', '0.749391727493917', '0.332632840343994',    '0.144927536231884', '0.102040816326531' ]

    extraIntegrationArrayNames =   [ 'akafield', 'akbfield', 'akcfield', 'akdfield', 'akefield',    'akffield', 'akgfield', 'akhfield', 'akifield', 'akjfield' ]

    isCrossCapable = False

    integrationOrder = 9.0

    _mainCheetahMethod_for_RK9Stepper = 'writeBody'

## END CLASS DEFINITION

if not hasattr(RK9Stepper, '_initCheetahAttributes'):
    templateAPIClass = getattr(RK9Stepper,
                               '_CHEETAH_templateClass',
                               Template)
    templateAPIClass._addCheetahPlumbingCodeToClass(RK9Stepper)


# CHEETAH was developed by Tavis Rudd and Mike Orr
# with code, advice and input from many other volunteers.
# For more information visit https://cheetahtemplate.org/

##################################################
## if run from command line:
if __name__ == '__main__':
    from Cheetah.TemplateCmdLineIface import CmdLineIface
    CmdLineIface(templateObj=RK9Stepper()).run()